Sparse Contour Representations of Sound

Abstract

Abstract-Many signals are naturally described by continuous contours in the time-frequency plane, but standard time-frequency methods disassociate continuous structures into isolated "atoms" of energy. Here we propose a method that represents any discrete time-series as a set of time-frequency contours. The edges of the contours are defined by fixed points of a generalized reassignment algorithm. These edges are linked together by continuity such that each contour represents a single phase-coherent region of the timefrequency plane. By analyzing the signal across many time-scales, an over-complete set of contours is generated, and from this redundant set of shapes the simplest, most parsimonious forms may be selected. The result is an adaptive time-frequency analysis that can emphasize the continuity of long-range structure. The proposed method is demonstrated with a few examples.

Long-range Order in Canary Song

“…The spectral density image provides a quantitative representation of syllable form and its variability across multiple renditions. In the spectral density image, color scale indicates the probability of finding a time-frequency contour [25] at a given point in the time-frequency plane. For a few syllables, visual inspection of the spectral density image revealed no variation for syllables drawn from different phrase duration bins ( Fig.…”

“…For a collection of syllables, we first generate a sparse time-frequency representation of each syllable using auditory contours [25]. Auditory contours provide a high-resolution binary image consisting of sparse, continuous lines that follow the features of the sound with high precision.…”

Phonocardiogram Signal Denoising Based on Nonnegative Matrix Factorization and Adaptive Contour Representation Computation

“…In what follows, the STFT of signal x using the same Gaussian window g as previously is denoted by V g x , and the principle of ACRC appliedŝ 1,LP F is detailed hereafter. ACRC technique is based on the projection, in some specific direction, of the reassignment vector (RV) defined by [23].…”

An Adaptive Computation of Contour Representations for Mode Decomposition

“…Indeed, we have just seen that RV points to the ridge associated with the TF signature of a mode, which means that, when crossing a ridge, RV undergoes a strong variation in its orientation. To determine the location of these sudden orientation changes, a first strategy was developed in [16], and consisted in projecting RV in a specific direction, given by an angle θ, and then in determining the location of the sign change of the projection. Thus, contour points (CPs) were defined as the zeros of RV (t, ω), v θ , where v θ is the unit vector in the direction θ, and ., .…”

“…The type of modes sought conditions of the technique for TF signatures estimation: some approaches concentrate on ridge detection for AM/FM modes [14], [15], while some others, using the properties of the reassignment vector (RV), can handle a wider class of TF signatures, the constraints on the modes being less stringent [16] [17]- [19]. In this latter case, the estimated TF signatures are then used to define basins of attraction (BAs) for the modes enabling their reconstruction.…”